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X₃₁₄₄¶

X₂₂₅-CEVA CONJUGATE OF X₄

X₃₁₄₄ (X₂₂₅-CEVA CONJUGATE OF X₄) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3144 = X_225-CEVA CONJUGATE OF X_4."""

        from __future__ import annotations

        from pathlib import Path

        import sympy.geometry as spg
        from geometor.model import Model

        from geometor.etc.ops import (
            central_line,
            centroid_of,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_barycentric_point,
            eval_trilinear_point,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03144(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3144 = X_225-CEVA CONJUGATE OF X_4 on reference triangle ABC."""
            X_3144 = eval_barycentric_point(model, A, B, C, '((a**(3) + 2*a**(2)*(b + c) + a*b*c - b**(3) - c**(3))/(b**(2) + c**(2) - a**(2)))', ID="X_3144", classes=["selected", "target"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center"])
            central_line(model, X_2, X_3, 2, 3)
            X_34 = eval_trilinear_point(model, A, B, C, '1 - sec(A)', ID="X_34", classes=["center", "incident"])
            X_978 = eval_trilinear_point(model, A, B, C, 'a**(2)*(b + c) + a*(b**(2) - b*c + c**(2)) - b*c*(b + c)', ID="X_978", classes=["center", "incident"])
            central_line(model, X_34, X_978, 34, 978, incident=True)
            X_225 = eval_trilinear_point(model, A, B, C, '(sec(A))*(cos(B) + cos(C))', ID="X_225", classes=["center", "incident"])
            X_1247 = point_from_barycentrics(model, A, B, C, 0.47979502, 0.29838347, 0.22182151, ID="X_1247", classes=["center", "incident"])
            central_line(model, X_225, X_1247, 225, 1247, incident=True)
            return promote_point_to_top(model, X_3144)


        def build_model(
            sides: tuple[float, float, float] = (5.0, 6.0, 7.0),
            show_guides: bool = False,
        ) -> Model:
            """Build a `geometor.model.Model` for X_3144 on the given reference triangle."""
            model = create_model('X_3144 = X_225-CEVA CONJUGATE OF X_4')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03144(model, A, B, C)
            return model


        if __name__ == "__main__":
            here = Path(__file__).resolve().parent
            model_acute = build_model((5.0, 6.0, 7.0))
            model_acute.save(str(here / "x-03144.json"))
            write_center_svg(
                model_acute,
                here / "x-03144.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3144¶

X₃₁₄₄¶